Solve x^2+xy+y=24xy

$$x ^ { 2 } + x y + y = 24 x y$$

Solve for y

$$y=-\frac{x^{2}}{1-23x}$$

$$x\neq \frac{1}{23}$$

Steps for Solving Linear Equation

Subtract 24xy from both sides.

$$x^{2}+xy+y-24xy=0$$

Combine xy and -24xy to get -23xy.

$$x^{2}-23xy+y=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-23xy+y=-x^{2}$$

Combine all terms containing y.

$$\left(-23x+1\right)y=-x^{2}$$

The equation is in standard form.

$$\left(1-23x\right)y=-x^{2}$$

Divide both sides by -23x+1.

$$\frac{\left(1-23x\right)y}{1-23x}=-\frac{x^{2}}{1-23x}$$

Dividing by -23x+1 undoes the multiplication by -23x+1.

$$y=-\frac{x^{2}}{1-23x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y\left(529y-4\right)}+23y}{2}$$

$$x=\frac{-\sqrt{y\left(529y-4\right)}+23y}{2}$$

Solve for x

$$x=\frac{\sqrt{y\left(529y-4\right)}+23y}{2}$$

$$x=\frac{-\sqrt{y\left(529y-4\right)}+23y}{2}\text{, }y\geq \frac{4}{529}\text{ or }y\leq 0$$